What is the Greatest Common Factor of 20385 and 20400?

Greatest common factor (GCF) of 20385 and 20400 is 15.

GCF(20385,20400) = 15

We will now calculate the prime factors of 20385 and 20400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20385 and 20400.

How to find the GCF of 20385 and 20400?

We will first find the prime factorization of 20385 and 20400. After we will calculate the factors of 20385 and 20400 and find the biggest common factor number .

Step-1: Prime Factorization of 20385

Prime factors of 20385 are 3, 5, 151. Prime factorization of 20385 in exponential form is:

20385 = 3³ × 5¹ × 151¹

Step-2: Prime Factorization of 20400

Prime factors of 20400 are 2, 3, 5, 17. Prime factorization of 20400 in exponential form is:

20400 = 2⁴ × 3¹ × 5² × 17¹

Step-3: Factors of 20385

List of positive integer factors of 20385 that divides 20385 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 151, 453, 755, 1359, 2265, 4077, 6795

Step-4: Factors of 20400

List of positive integer factors of 20400 that divides 20385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20385 and 20400. The biggest common factor number is the GCF number.
So the greatest common factor 20385 and 20400 is 15.

Also check out the Least Common Multiple of 20385 and 20400